Linear and circular solvent penetration experiments are used to study the dissolution of anionic SLE3S surfactant mesophases in water. We show that a lamellar (Lα) phase in contact with water will transit through a series of cubic, hexagonal, and micellar phase bands with sharp interfaces identified from their optical textures. In both linear and circular geometries, the kinetics of front propagation and eventual dissolution are well described by diffusive penetration of water, and a simple model applies to both geometries, with a different effective diffusion coefficient for water Df as the only fitting parameter. Finally, we show a surprising variation of dissolution rates with initial surfactant concentration that can be well explained by assuming that the driving force for solvent penetration is the osmotic pressure difference between neat water and the aqueous fraction of the mesophase that is highly concentrated in surfactant counterions.